I'm not quite clear on the final practical step though-- do you avoid the multiple messages and circular references by making the person doing the mailing manually clean up their list, or could you solve the problem by resolving all distribution lists to their "final" addresses and selecting the distinct address?

This work was motivated by a problem I had with a marketing company in Vancouver, where the database administrator was frequently interrupted by requests to fix their broadcasts. Although there weren't a lot of errors given the size of the weekly mailouts, each one was a serious annoyance that consumed a lot of time.

It took a while before I realized that their problems were simply anomalies in directed graphs, which made things easier to visualize.

But for really large graphs, we might need a more efficient way to process them.

But it seems a simpler way of dealing with your problem is to change your e-mail broadcast system internally. Instead of the broadcast system every broadcasing to a list, have it expand all lists and remove all duplicates at the time it is sent. That way a broadcast list never receives anything from another internal broadcast list and no person ever receives a message twice. Am I missing something?

I should have made a subtle distinction between mailing lists and re-directions. Although the latter may be viewed as a special case of the former, you can't delete someone's re-direction on the email server just because it causes conflicts elsewhere.

Suppose we have one broadcast submitted by Arnold:

A --> bA --> c

and two re-directions submitted individually by Bob and Calvin (which you can't delete because these people don't want ANY emails):

b --> Ac --> b

Althoug A is a valid email address, it's meant to represent a mailing list (eg. customers@myCompany.com) while b, c are real people (eg. Bob@myCompany.com).

There are no duplicates in this list, but both circularity and redundancy exist.

We could remove the second re-direction, but then Calvin would start getting emails.

If we expand mailing lists on the right hand side, we would get:

A --> bA --> cb --> bb --> cc --> b

Eliminating self re-directions gets us:

A --> bA --> cb --> cc --> b

Since we can't eliminate the last re-direction submitted individually by Calvin, how do we get rid of the duplicates on the right hand side? We could eliminate b --> c, but then Bob's now getting emails.

Already my head's spinning.

You may be correct in your approach, but it looks a bit messy (to me, anyway).

That's why I viewed these things as graphs, where mailing lists and re-directions are the same thing.

Yes, that makes sense in that situation. If redirection, and not simply mailing lists that need to be expanded, then you could wind up with a circular reference like that that would be awkward and with no clean way to resolve it automatically.